If the flight is not overbooked, the airline loses revenue from empty seats, but if too many seats are sold, the airline loses money from the compensation it must pay to the bumped passengers.

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American Airlines Flight 171 from New Yorks’ JFP airport to LAX airport in Los Angeles uses an Airbus A321 aircraft with 189 seats available for passengers. American Airlines can overbook by accepting more reservations than there are seats available. If the flight is not overbooked, the airline loses revenue from empty seats, but if too many seats are sold, the airline loses money from the compensation it must pay to the bumped passengers. Assume that there is a 0.0995 probability that a passenger with a reservation will not show up for the flight (based on data from the IBM research paper “Passenger-Based Predictive Modeling of Airline No-Show Rates” by Lawrence, Hong, and Cherrier). Also assume that American Airlines accepts 205 reservations for the 189 seats that are available and that passengers are independent of each other.
Using StatCrunch’s calculators, find the probability that when 205 reservations are accepted for American Airlines Flight 171, there are more passengers showing up than there are seats available. Is the probability of overbooking small enough that it does not happen very often, or does it seem too high so that changes must be made to make it lower?
Use trial and error to find the maximum number of reservations that could be accepted so that the probability of having more passengers than seats is 0.05 or less.
What do you think about this policy of overbooking flights? Is it a good thing, a bad thing, or a little of both? Why do you think that?

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